Computation of convex bounds for present value functions with random payments

Some limiting properties of the bounds of the present value function of a life insurance portfolio

“…However, in Ahcan et al (2006), T l in S n was taken to be l, not random variable. As reflected in model (1.1), recently the effects of stochastic interest rates have been emphasized in the life insurance literature because "durations of contracts in life insurance and the life annuity business are typically very long (often 30 or even more years) and the financial and investment risk-unlike the mortality risk-cannot be diversified with an increase in the number of policies" (Hoedemakers et al (2006)). In the actuarial literature there are many papers covering the random interest rates.…”

Some limiting properties of the bounds of the present value function of a life insurance portfolio

“…This technique was proposed by Dhaene and Goovaerts (1996), (1997) and adopted by Wang and Dhaene (1998), Goovaerts and Redant (1999), Goovaerts and Dhaene (1999), Dhaene et al (2002a), (2002b), Goovaerts et al (2000), Simon et al (2000), Vyncke et al (2001), Kaas et al (2000), (2001), Ahcan et al (2006), and others.…”

“…It is noteworthy that Ahcan et al (2006) considered a model similar to model (1.1) and presented the convex upper and lower bounds for S n . However, in Ahcan et al (2006), T l in S n was taken to be l, not a random variable.…”

“…We refer the reader to Kaas et al (2000) for the proof of part 1, and to Ahcan et al (2006) for the proof of part 2. Dhaene et al (2002b) …”

Asymptotics for Risk Measures of Extreme Risks

“…We distinguish the cases k = 1 and k > 1. For the case k = 1, applying Lemmas 3.5 and 2.15 (2) to relation (3.3) we have…”